1. Compiler Exploitation of Decimal Floating-Point Hardware Ian McIntosh, Ivan Sham IBM Toronto Lab

2. Why do we need Decimal Floating Point? Microsoft® Office Excel 2003

3. …Why do we need Decimal Floating Point? public static double calculateTotal(double price, double taxRate) { return price * (1.00 + taxRate); }... System.out.println("Total: $" + calculateTotal(7.0, 0.015)); ----------------------------------------- Output -> Total: $7.1049999999999995

4. Outline IEEE Decimal Floating Point (DFP) C/C++ and DFP Java and DFP

5. What is IEEE 754-2008 Decimal Floating Point? Type NameSizePrecisionExponent Range decimal32 32 bits 4 bytes 7 digits single -101 to +90 decimal64 64 bits 8 bytes 16 digits double -398 to +369 decimal128 128 bits 16 bytes 34 digits quad -6176 to +6111

6. What is Decimal Floating Point? Values use base 10 digits –Alternative to Binary Floating Point Digits continuation Exponent continuation Combination field Sign Sign bit Combination field – encodes the first two bits of the exponent and the leftmost digit (BCD) Exponent continuation – encodes the remaining biased exponent bits Digits continuation – encodes the remaining digits in DPD 3-digit block form -1/1010100010010000000000000000000001

7. Why should we use DFP? Pervasive –Decimal arithmetic is almost universal outside computers More accurate for decimal numbers – Can represent “important” numbers exactly Programming trend –IEEE 754, IEEE 854, IEEE 754R, IEEE 754-2008

8. Why should we use DFP? Easier to convert to/from strings –Great for working with databases Performance –More on this later

9. Why avoid using DFP? It’s new and different Not all languages include DFP Limited support by other vendors Software implementations can be slow Incompatible formats (DPD and BID) Current IBM hardware is in most cases slower than binary floating point (BFP)

10. DFP at IBM Hardware –POWER6 and Z10 Microcode in Z9 –One DFP functional unit Non-pipelined Software –XL C, XL C++, gcc, PL/I –IBM® Developer Kit for Java™ 6

11. C Example – Without DFP double calculateTotal(double price, double taxRate) { return price * (1.00 + taxRate); }... printf ("Total: $%19.16f\n", calculateTotal(7.0, 0.015)); ------------------------------------------- Output -> Total: $7.1049999999999995

12. C Example – With DFP _Decimal64 calculateTotal(_Decimal64 price, _Decimal64 taxRate) { return price * (1.00dd + taxRate); }... printf ("Total: $%19.16Df\n", calculateTotal(7.0dd, 0.015dd)); ------------------------------------------- Output -> Total: $7.1050000000000000

13. C / C++ DFP C / C ++ Type Name C ++ Class Name Literal Suffix C printf / scanf Format Modifier Library Function Suffix _Decimal32 decimal32 dfHDd32 _Decimal64 decimal64 ddDd64 _Decimal128 decimal128 dlDDd128

14. C / C++ DFP – Approaches C syntaxEasiest and most natural. On AIX can be compiled to either use POWER 6 DFP instructions or call decNumber library. On z/OS uses DFP instructions. DFPAL libraryAutomatically adapts to either using DFP instructions or calling decNumber. decNumber libraryVery portable library. decFloat libraryNewer and often faster library. decNumber++ libraryC ++ DFP class library.

15. C/C++ DFP Performance – Product and Sum In a loop:a[i] += b[i] * c[i]; noopt-O2-O3 C syntax using decNumber library (Baseline) 1.26x faster than noopt 2x faster than noopt C syntax using DFP instructions 27x faster than software 1.82x faster than noopt 39x faster than software 4.37x faster than noopt 59x faster than software Measured by Tommy Wong, Toronto Lab xlc for AIX version 9 on POWER 6

16. C/C++ DFP Performance – C telco Benchmark DFPAL* calls using decNumber(Baseline) decNumber calls1.92x faster DFPAL* calls using DFP instructions2.56x faster C syntax using DFP instructions4.4x faster Measured by Tommy Tse, Beaverton xlc for AIX version 9 on POWER 6 using -O2 * DFPAL automatically adapts to either using DFP instructions or calling decNumber.

17. Decimal Floating Point in Java IBM Developer Kit for Java 6 64 bit DFP via BigDecimal class library POWER 6 server or Z10 mainframe

18. BigDecimal Class Library arbitrary-precision signed decimal numbers –an arbitrary precision integer unscaled value –32-bit integer scale Supports all basic arithmetic operations Complete control over precision and rounding behavior 92183021.23431 Unscaled value: 9218302123431 Scale: 5

19. BigDecimal and DFP BigDecimal can represent arbitrary significance but 64-bit DFP restricted to 16 digits BigDecimal represents 32-bit exponent, 64-bit DFP restricted to 10 bits Values that cannot be represented as DFP DFP values that can be represented values Set of all BigDecimal objects

20. BigDecimal Representation Problem Want to: –Use DFP representation –Avoid software re-try BigDecimal a = new BigDecimal("9876543210123456", MathContext.DECIMAL64); BigDecimal b = new BigDecimal("1234567890987654", MathContext.DECIMAL64); BigDecimal c = a.add(b); Fits in 64 bit DFP Precision overflow 64

21. Hysteresis Mechanism Choose best representation automatically –Base on history of operations Use counter and threshold –Bias towards DFP representation Division, string construction, unaligned addition –Bias towards software representation Compare, integer constructions BigDecimal constructors check counter

22. JIT Compiler Optimization Detects DFP hardware support –Replaces checks in java code with constant –Disables hysteresis mechanism when no DFP Inject DFP instructions –Load operands from BigDecimal Objects –Set rounding mode (if necessary) –Perform DFP operation –Reset rounding mode (if necessary) –Check result validity –Store result into BigDecimal Object

23. Example – Java / BigDecimal public static BigDecimal calculateTotal( BigDecimal price, BigDecimal taxRate) { return price.multiply(taxRate.add(BigDecimal.ONE)); }... System.out.println("Total: $" + calculateTotal( new BigDecimal(“7.00”), new BigDecimal(“0.015”)); ------------------------------------------- Output -> Total: $7.1050

24. Microbenchmark results HW DFP Speed up Unaligned Addition 5.05x Aligned Multiplication 3.03x Aligned Division 2.23x Half Even Rounding 1.45x String based construction 2.08x zLinux on Z10 using Java 6 SR2

25. Performance Improvement - Telco z/OS on Z10 using Java6 SR1

26. Summary Use DFP –Control over precision and rounding behaviour –Accuracy for decimal numbers –Programming trend High performance for suitable workloads –DFP hardware can greatly improve performance –4x (2x) speedup was measured on C (Java) for Telco

27. Thank you! IBM Toronto Software Lab Ian McIntosh ianm@ca.ibm.comianm@ca.ibm.com Ivan Sham ivansham@ca.ibm.comivansham@ca.ibm.com

28. Resources General Decimal Arithematic –http://www2.hursley.ibm.com/decimal/http://www2.hursley.ibm.com/decimal/ Decimal floating-point in Java 6: Best practices –https://www.304.ibm.com/jct09002c/partnerworld/wps/serv let/ContentHandler/whitepaper/power/java6_sdk/best_pra cticehttps://www.304.ibm.com/jct09002c/partnerworld/wps/serv let/ContentHandler/whitepaper/power/java6_sdk/best_pra ctice

29. Java command line options -Xdfpbd –Disables the hysteresis mechanism -Xnodfpbd –Disable DFP support and hysteresis mechanism

30. Hysteresis Mechanism Performance Multi-threaded transaction base benchmark –Workload does not use MathContext64 zLinux on Z10 using Java 6 SR2

31. Java Telco Performance on POWER6 AIX on POWER6 using Java 6